Doppler radar spectral width broadening due to beamwidth and wind shear

The spectral width observed by Doppler radars can be due to several effects including the atmospheric turbulence within the radar sample volume plus effects associated with the background flow and the radar geometry and configuration. This study re-examines simple models for the effects due to finite beam-width and vertical shear of the horizontal wind. Analytic solutions of 1- and 2-dimensional models are presented. Comparisons of the simple 2-dimensional model with numerical integrations of a 3-dimensional model with a symmetrical Gaussian beam show that the 2-dimensional model is usually adequate. The solution of the 2-dimensional model gives a formula that can be applied easily to large data sets. Analysis of the analytic solutions of the 2-dimensional model for off-vertical beams reveals a term that has not been included in mathematical formulas for spectral broadening in the past. This term arises from the simultaneous effects of the changing geometry due to curvature within a finite beamwidth and the vertical wind shear. The magnitude of this effect can be comparable to that of the well-known effects of beam-broadening and wind shear, and since it can have either algebraic sign, it can significantly reduce (or increase) the expected spectral broadening, although under typical conditions it is smaller than the beam-broadening effect. The predictions of this simple model are found to be consistent with observations from the VHP radar at White Sands Missile Range, NM.     

The Pleistocene history of Wales and the borderland

The Pleistocene rock-stratigraphic record is accorded more or less traditional time-stratigraphic interpretation which was held widely before application of an Irish developmental model in 1960. The following sequence of events are recognised: (1) Complete glaciation, of indeterminate age, which antedated the raised beach interglacial. (2) The raised beach episode which is shown to be the last (Ipswichian) interglacial. (3) The last (Devensian/Weichselian) glaciation, followed by possible readvance in northwest and northeast Wales; prior and subsequent to glaciation periglacial conditions obtained. It is shown that the Irish model, relying heavily as it does on the equation of rock and time stratigraphy, is inapplicable in Wales.